Ehrhart polynomial for non-full dimensional polytopes

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josephineyu
Posts: 6
Joined: 05 Aug 2012, 20:51

Ehrhart polynomial for non-full dimensional polytopes

Postby josephineyu » 04 Dec 2015, 17:36

Hi,
For lattice polytopes that are not full dimensional , EHRHART_POLYNOMIAL_COEFF outputs something strange. First applying ambient_lattice_normalization does the right thing, so I would expect polymake to do this instead. Perhaps EHRHART_POLYNOMIAL_COEFF assumes the input polytope to be full-dimensional. If it is the case, then it should be stated in the tutorial/documentation here:
http://polymake.org/doku.php/tutorial/l ... s_tutorial
--Josephine

blorenz
Developer
Posts: 139
Joined: 10 Jan 2011, 17:21

Re: Ehrhart polynomial for non-full dimensional polytopes

Postby blorenz » 07 Dec 2015, 19:54

Hello,

thank you very much for the report. The Ehrhart polynomial is designed to work with non-full-dimensional polytopes as well. But there is a bug with the zero-padding of the H_STAR_VECTOR that, in this case, causes the conversion to the Ehrhart polynomial to go wrong.

The H_STAR_VECTOR should always be correct, the EHRHART_POLYNOMIAL_COEFF should be correct if you have LattE configured and preferred.
A somewhat ugly workaround which does not need the lattice normalization would be:

Code: Select all

print binomial_to_power_basis(new Vector($p->H_STAR_VECTOR->slice(0,$p->CONE_DIM)));
This will be fixed in the the next snapshot and release and I could also prepare a patch for the current release on request.

Best,
Benjamin

josephineyu
Posts: 6
Joined: 05 Aug 2012, 20:51

Re: Ehrhart polynomial for non-full dimensional polytopes

Postby josephineyu » 10 Dec 2015, 15:27

Thanks, Benjamin! This will work for now.
Josephine


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